Construction of Smooth Refinable Function Vectors by Cascade Algorithms

2002 ◽  
Vol 40 (4) ◽  
pp. 1354-1368 ◽  
Author(s):  
Di-Rong Chen
Keyword(s):  
Refinable Function ◽  
Cascade Algorithms ◽  
Refinable Function Vectors

scholarly journals Generalized interpolating refinable function vectors

2009 ◽  
Vol 227 (2) ◽  
pp. 254-270 ◽  
Author(s):  
Bin Han ◽  
Soon-Geol Kwon ◽  
Xiaosheng Zhuang
Keyword(s):  
Refinable Function ◽  
Refinable Function Vectors

scholarly journals High Balanced Biorthogonal Multiwavelets with Symmetry

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Youfa Li ◽  
Shouzhi Yang ◽  
Yanfeng Shen ◽  
Gengrong Zhang
Keyword(s):  
General Scheme ◽  
Refinable Function ◽  
Antisymmetric Component ◽  
Multiwavelet Transform ◽  
Refinable Function Vectors ◽  
Function Vector ◽  
Biorthogonal Multiwavelets ◽  
Vector Valued

Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. Yang et al. (2006) constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results.

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